Mathbee CBSE Mathbee · CBSE Class 12 Maths
NCERT Class 12 · Ch 11 Miscellaneous Exercise · Q3

NCERT Class 12 Maths · Chapter 11 Three Dimensional Geometry · Miscellaneous Exercise Question 3

Find k so directions of (x−1)/(−3)=(y−2)/(2k)=(z−3)/2 and (x−1)/(3k)=(y−1)=(z−6)/(−5) are orthogonal.

💡 Concept Hints

  1. Identify the base point and a nonzero direction before applying a vector formula.
  2. Use dot products for angles, proportional directions for parallelism, and a triple product for skew-line distance.

✅ Step-by-Step Solution

Final Answer: k=−10/7.
  1. The directions are (−3,2k,2) and (3k,1,−5).
  2. Their dot product is −9k+2k−10=−7k−10.
  3. Setting this to zero gives k=−10/7, nonzero as required by the denominators.

Master Chapter 11: Three Dimensional Geometry

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Three Dimensional Geometry.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Find a line parallel to the x-axis and passing through the origin.
Next Question →
Find the shortest distance between r=(6,2,2)+t(1,−2,2) and…

All Questions in Three Dimensional Geometry — Miscellaneous Exercise

Q1Q2Q3Q4Q5

Related Questions in Three Dimensional Geometry

Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the foot of the perpendicular from (2,−3,4) to the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles α,β,γ with the positive coordinate axes. Find cos 2α+cos 2β+cos 2γ.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the distance of (α,β,γ) from the y-axis.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find direction cosines of (x−1)/2=(1−y)/3=(2z−1)/12.
Class 12 Three Dimensional Geometry · Mcq Single Correct
Find the acute angle between two distinct body diagonals of a cube.
Class 12 Three Dimensional Geometry · Mcq Single Correct
A line makes angles θ₁,θ₂,θ₃,θ₄ with the four body diagonals of a cube. Find Σ cos²θᵢ.